Lagrangean relaxation based heuristics for lot sizing with setup times

• Published in: European journal of operational research 2009-04, Vol.194 (1), p.51-63
• Main Authors: Süral, Haldun, Denizel, Meltem, Van Wassenhove, Luk N.
• Format: Article
• Language: English
• Subjects: Applied sciences; Branch & bound algorithms; Exact sciences and technology; Heuristic; Inventory; Inventory control; Inventory control, production control. Distribution; Inventory Setup time Reformulation Lagrangean relaxation Heuristic; Lagrange multiplier; Lagrangean relaxation; Operational research and scientific management; Operational research. Management science; Optimization algorithms; Reformulation; Setup time; Studies
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2007.11.052

We consider a lot sizing problem with setup times where the objective is to minimize the total inventory carrying cost only. The demand is dynamic over time and there is a single resource of limited capacity. We show that the approaches implemented in the literature for more general versions of the problem do not perform well in this case. We examine the Lagrangean relaxation (LR) of demand constraints in a strong reformulation of the problem. We then design a primal heuristic to generate upper bounds and combine it with the LR problem within a subgradient optimization procedure. We also develop a simple branch and bound heuristic to solve the problem. Computational results on test problems taken from the literature show that our relaxation procedure produces consistently better solutions than the previously developed heuristics in the literature.